Three specific nonparametric statistical problems will be investigated in this research project. A) In comparing two treatments, subjects come to the experiment sequentially and must be treated at once. Suppose that a restricted randomization scheme was employed to assign subjects to treatment groups. The problem is how to analyze the data observed from the subjects based on a randomization model. B) In the statistical analysis of paired observations, often times there are missing values on either of the variables. An interesting problem is how to use all the data points (complete and incomplete pairs) in the most efficient way for the analysis. C) The principal investigator is interested in obtaining estimators (e.g. the maximum likelihood estimator) of the distribution function by imposing some reasonable conditions on the life expectancy function in the presence of censoring variables so that, unlike the Kaplan-Meier estimate, the resulting estimators are well defined on the entire real line.